Computer for dividing one variable quantity by another



J. l... BARKER Sept. 12, 1967 COMPUTER FOR DIVIDING ONE VARIABLE QUANTITY BY ANOTHER Original Filed Sept.

INVENTOR.

JOHN L. BARKER BY mmnEOIHV ATTORNEY United States Patent 3,341,698 COMPUTER FOR DIVIDING ONE VARIABLE QUANTITY BY ANOTHER John L. Barker, Norwalk, Conn., assignor to Laboratory for Electronics, Inc, Waltham, Mass., a corporation of Delaware Original application Sept. 8, 1960, Ser. No. 57,864, now Patent No. 3,239,653, dated Mar. 8, 1966. Divided and this application June 7, 1965, Ser. No. 461,836

7 Claims. (Cl. 235-196) This invention relates generally to computing devices, and more particularly to a device for dividing two variable quantities.

This application is a division of my co-pending US. application, S.N. 57,864, filed Sept. 8, 1960, which in turn is a continuation-in-part of my original US. application S.N. 816,966, filed May 29, 1959, which original application is abandoned. The said co-pending application S.N. 57,864 issued Mar. 8, 1966 as US. Patent 3,239,653. The subject matter of the present application is common to said co-pending application and to said original application.

The co-pending application and said original application, relate to a traffic density computer which computes the density of trafiic moving along a roadway by dividing the output of a traflic volume computer by the output of a traflic speed computer.

Traflic volume is defined as the number of vehicles passing a given point during a specified period of time and is usually measured in vehicles per hour. Trafiic speed is the speed of vehicles flowing upon a roadway, usually measured in miles per hour. Trafiic density is measured in number of vehicles per unit length of roadway, which is usually vehicles per mile.

The means for computing trafiic volume and for computing trafiic speed and interrelating these as well as means for dividing trafiic volume by traffic speed to obtain traffic density are disclosed in said co-pending application, S.N. 57,864 and in said abandoned application S.N. 816,966 and reference may be had to said applications for further explanation.

Reference may also be had to US. Patent 3,059,232, issued Oct. 16, 1962, referred to as a co-pending application Ser. No. 732,248 filed May 1, 1958, in said original application S.N. 816,966 and in said application S.N. 57,864 filed Sept. 8, 1960.

Various aspects of a trafiic density computer and other features interrelating traflic volume and traflic speed are disclosed and claimed in said co-pending application S.N. 57,864.

The present application relates to apparatus for dividing one quantity by another, which, by way of example, may be used in the density computer of the co-pending application.

Thus reference is made from time to time in the present application to trafiic volume as an example of a quantity which may represent a dividend, and to traflic speed as an example of a quantity which may represent a divisor and to traflic density as an example of a quantity which may represent a quotient.

It is therefore, a general object of this invention to provide an improved device for dividing two variable quantities.

Patented Sept. 12, 1967 Referring now to the single figure of drawings, which represents a schematic diagram of the apparatus according totthe invention, the inputs to the system may be an electrical voltage input, represented by El, as a dividend input, between line 78' and ground in block 2, and an electrical voltage input E2 or E2 or a mechanical input such as the position of a potentiometer arm, 76, as a divisor input. By way of example the dividend input E1 may represent the trafiic volume voltage output of a traflic volume computer and the divisor input E2 or E2, or the position of arm 76, may represent the trafiic speed output of a speed average computer.

In the case of an electrical input for the divisor, this is represented by a voltage input E2, between ground and the lower input of chopper 66 in block 1. The arm 76 of potentiometer 74 in block 2 is mechanically controlled by the broken line linking arm 76 in block 2 with arm 64 and servo motor 68 in block 1, as more fully described below, so that the position of the arm 76 along the resistance 74 of the potentiometer represents the input electrical voltage E2 or trafiic speed.

Referring now to the part of the schematic diagram in block 1, the lower of two inputs to the chopper 66 may be an electrical voltage E2 as a divisor as pointed out above, and may correspond to a new average speed from a capacitor 65 via a relay contact 51a not shown here, but shown and described in said applications S.N. 816,966 and S.N. 57,864. The other input to chopper 66 is the previous average appearing at point 62, which indicates by the mechanical position of the arm 64 a voltage corresponding to the divisor or speed average. The output of the chopper 66 is connected to a servo amplifier 67 which in turn will drive servo motor 68 to control the position of arm 64.

The chopper 66 simply alternately connects between its two inputs, and if there is a diiference between the two inputs, an alternating current (AC) wave is received on the output. If there is no difference, it makes no difference which signal is connected to the output which feeds the servo-amplifier. The output of the chopper is an AC. voltage which is proportional to the difference between the new average and the old average and it is phased such that after it is amplified, it will drive servo motor 68 in the proper direction. The other phase connection of the servo motor is not shown, but is connected to 60 cycle power for example. If the voltage on arm 64 which is connected to the upper input at 62 to chopper 66 is designated E2, and if the new voltage E2 is higher than the old voltage E2, the motor will drive clockwise, and if it is lower, it will drive counterclockwise.

The servo amplifier 67 drives the servo motor 68, which in turn drives the potentiometer arm 64 so as to make the average voltage E2 appearing at 62 equal to the new voltage E2.

The volume or dividend voltage E1 must be divided by speed or divisor voltage E2 to obtain density or quotient voltage E3. In order to do this, a value of density or quotient voltage E3 is assumed and is multiplied by speed or divisor voltage E2 or E2 and the result is compared with the measured value of volume or input dividend voltage E1. The error is used to adjust the assumed value of density or quotient voltage E3 until the error is reduced to a minimum and the value of density or quotient voltage E3 read.

Potentiometer 74 is shown in block 2 and the voltage on the potentiometer represents the assumed density or quotient voltage E3. The arm 64 in block 1 corresponding to the speed or divisor E2 is mechanically coupled to arm 76 of potentiometer 74. What may be considered an assumed density or quotient voltage E3 is present across potentiometer 74. This is multiplied by the speed or divisor voltage E2, as represented by the position of arm 76 along the resistance winding of potentiometer 74. Thus, the voltage on arm 76 represents E2 times E3 and can be considered a trial dividend voltage.

Diodes 77 and 78 are connected in series, and one end of these diodes returns to the volume or dividend input voltage E1 via lead 78'. The other end of the diode combination is connected to arm 76 through limiting resistor 79'. If the computed volume or dividend input voltage E1 is lower than the trial volume dividend voltage appearing on arm 76, current will flow through diodes 77 and 78, and the impedance of the junction of the two diodes will be relatively low. If the trial volume or dividend voltage is lower than the computed volume or dividend input voltage, there will be no current flowing through the diodes, and therefore the junction of the diodes can be assumed to be a high impedance point. The junction is indicated by the numeral 79 and is coupled through capacitor 80 and resistor 81 to a source of A.'C. voltage. If the junction 79 is at a high impedance indicating that the trial volume or dividend voltage is lower than the computed volume or input dividend voltage,the voltage at the point of the junction will follow the AC. voltage applied to the resistor 81. That being the case, that same A.C. voltage will be applied to the input of amplifier 82.

Now where there is current flowing between the junction of the diodes as when the trial voltage or arm 76 is higher than the computed or input dividend voltage E1 the A.C. that is applied to resistor 81 and also the input to the amplifier will all be absorbed. Therefore, if the impedance of the junction is low, there is no input to the amplifier or a very small input to the amplifier, and therefore there will be no A.C. on the output of the amplifier. If the impedance of the junction is high, the output of the amplifier will be high.

If the trial volume or trial dividend voltage appearing at 76 is lower than the computed volume or input dividend voltage E1, the'output of the amplifer 82 will be high and through diode rectifier 83 via lead 83' will be applied to the upper side of potentiometer 74 and will raise the assumed value of the density or quotient voltage E3 appearing across potentiometer 74. If the output of the amplifier is high, then the input signal to the amplifier is lowered because the trial volume or trial dividend volt-age would have been high, causing the impedance at the junction of the diodes to be low, and therefore a low input signal to amplifier 82 which reduces the assumed density or quotient voltage E3.

The gain of amplifier 82 is very high so that the error is always insignificant, even when the values change a factor of ten to one. For example, if the gain is 100,000 in the amplifier, the error would be 0.001 to one percent in the density*that is being computed. If the gain is 10,000, the error would be 0.01 to one percent. As an example, assume that the volume computed or dividend input voltage E1 remains the same and the speed or divisor input changes. Under those conditions, assuming the speed or divisor goes down, then the factor of density or quotient times speed or divisor will be lowered and the trial volume or trial dividend will go down, causing the diodes to not conduct. The junction 79 now becomes a high impedance and it is necessary then to raise the density or quotient. In other words, this high impedance point allows more signal input into the amplifier 82 which raises the density or quotient voltage and raises then the trial volume or trial dividend voltage and thatin-turn occurs until the trial volume or trial dividend voltage is close to the computed volume or input dividend voltage. The new density or quotient is higher because the speed or divisor is lower and the volume or dividend is the same value.

Now the converse of that will be true if the speed or divisor increased. A trial volume or trial dividend voltage would be present which Was higher than the computed volume or input dividend voltage and the input to the amplifier would be lower which in turn would reduce its output. The density or quotient voltage and the input to the potentiometer 74 would be lowered and the voltage on arm 76 will go down and the trial volume or trial dividend voltage again will go downuntil it is only slightly less than the computed volume or input dividend voltage and the condition of equilibrium has been achieved.

To summarize, in either case whether the potentiometer arm 76 is moved by change in speed or divisor or the voltage E1 changes because of a change in actual measured volume or input dividend, the substantial matching by the operation of the circuitry in block 2 of the trial volume or trial dividend and the computed volume or inputdividend results in having a value of the density or quotient on 74 which then can be taken as the density or quotient for that combination and is then read on meter 84.

The voltage value appearing at 84 can of course be connected to a meter as shown, or connected to other circuitry as desired. In this case, it can be connected to the input of the amplifier to do work. It could be used, for example, to drive work circuits associated with the determination of the cycle length on a traflic signal system, as more fully set forth in said co-pending application S.N. 57,864, for example.

Thus the input dividend voltage E1 may represent traffic volume, as the output of a traffic volume computer (such as the output of block 20 of said original application Ser. No. 816,966) for example; the input divisor position of the arm 76 or the electrical voltage E2 as a divisor input may represent traflic speed as the output of an average speed computer, (such as the output of block 21, or a part thereof as the lower input to chopper 66, in said application Ser. No. 816,966) for example, and the resulting quotient output voltage E3 may represent traffic density, for example.

Obviously, numerous changes in construction or rearrangements of parts might be resorted to without departing from the spirit of the invention as defined by the claims.

What I claim is:

1. A device for dividing two variable quantities including in combination:

a first input means for connection of a first electrical input representing the first of said quantities as a dividend,

a second input means for connection of a second electrical input representing the second of said quantities as a divisor,

a potentiometer having a resistance winding with one side connected to a reference point, and having a potentiometer arm,

a voltage comparison means having first and second inputs for connection .of two input voltages to provide an output proportional to the difference between said two voltages,

means coupled between said second input means and said potentiometer arm to position said arm along said resistance winding relative to said reference point in proportion to said second electrical input,

an electrical connection coupling said arm of said potentiometer to the first input of said voltage comparison means, 7 Y

a second electrical connection coupling said first input means to the second input of said voltage compari son means,

a high gain amplifier having an input coupled to said voltage comparison means output, said amplifier providing an output proportional to said difference signal, and

means including a rectifier for coupling the output of said amplifier to the other side of said resistance winding of said potentiometer to provide a voltage on said arm proportional to the product of said amplifier output voltage and said second electrical input as represented by the position of said arm of said potentiometer to reduce the difference between said voltage on said arm and said first electrical input to a low value, whereby the voltage across said potentiometer provides an electrical output proportional to a quotient.

2. A device for dividing two variable quantities including in combination:

first input means for connection of a first electrical input representing a first of said quantities as a dividend,

second input means for connection of a second electrical input representing the second of said quantities as a divisor,

a multiplying potentiometer having a resistance Winding with one side connected to a reference point, and having a potentiometer arm,

first and second diodes connected in series in the same polarity between said arm of said potentiometer and said first input means,

means coupled between said second input means and said potentiometer arm to position said arm along said resistance winding relative to said reference point in proportion to said second electrical input,

means including a high gain amplifier having an input coupled to the junction of said diodes, said amplifier providing an output proportional to the difference between the voltages on said arm and on said first input means, and

means including a rectifier for coupling the output of said amplifier to the other side of said resistance winding of said potentiometer to provide a voltage on said arm proportional to the product of said amplifier output voltage and said second electrical input as represented by the position of said arm on said resistance winding to reduce the difference between said voltage on said arm and said first electrical input to a low value, whereby the voltage across said potentiometer provides an electrical output proportional to the quotient.

3. A device as claimed in claim 2 in which said means coupled between said second input means and said multiplying potentiometer arm includes a chopper having first and second inputs and an output,

a further potentiometer having a resistance element adapted to be coupled across a source of direct current voltage and having an arm movable on said resistance element,

said first input of said chopper being coupled to said second input means,

said second input of said chopper being coupled to said arm of said further potentiometer,

said arm of said further potentiometer being mechanically coupled to said arm of said multiplying potentiometer,

servo-amplifier means coupled to the output of said chopper, and

servo-motor means coupled to said servo-amplifier to be driven by the output thereof to move said arms of said potentiometers,

said chopper deriving an electrical signal at its output proportional to the difference between its two inputs whereby said servo-motor will drive said arm of said further potentiometer to reduce said last-named difference to a low value to cause the voltage on said arm of said further potentiometer to be substantially equal to the input voltage at said second input means.

4. A device for divinding two variable quantities as claimed in claim 3 and including a capacitor connected between said other side of said multiplying potentiometer and said reference point, and

an output circuit connected from said other side of said multiplying potentiometer.

5. A device for dividing two variable quantities as claimed in claim 4 and including an indicating meter connected to said last-named output circuit.

6. A device for dividing effectively a first electrical input representing a dividend by a second electrical input representing a divisor, both inputs being variable to represent variable quantities, said device including in combination:

first input terminals for connection of said first electrical input, and

second input terminals for connection of said second electrical input,

a chopper having first and second inputs and an output, said first chopper input being connected to said second input terminals, said chopper output signal being proportional to the difference between voltages applied to its two inputs,

a first potentiometer connectable across a source of direct current voltage, said potentiometer having an arm connected to said second input of said chopper,

a servo-amplifier coupled to said output of said chopper,

a servo-motor coupled to said servo-amplifier to be driven thereby and coupled to said arm of said first potentiometer to position said arm to cause the voltage on said arm to approximate said input voltage at said second input terminal,

a second potentiometer having one end connected to a reference point and having an arm mechanically linked to the arm of said first potentiometer to be positioned along said second potentiometer in proportion to the output voltage of said chopper,

means including a pair of diodes connected in series in the same polarity between said arm of said second potentiometer and said first input terminals,

a source of alternating voltage,

a resistance having one end connected to said alternating voltage source,

a capacitor coupled between the other end of said resistance, and the junction of said diodes,

a high gain amplifier having an input and an output, the input coupled to said other end of said resistance, and

means including a rectifier coupled between the output of said amplifier and the other end of said second potentiometer to apply said amplifier output across said second potentiometer, whereby an electrical signal is developed at the input of said high gain amplifier proportional to the difference between the voltage at the arm of said second potentiometer and the voltage at said first input terminals,

said voltage on said arm of said second potentiometer representing a product of said high-gain amplifier output and said divisor input as a trial dividend and the voltage at said first input terminals representing the input dividend, said output of said amplifier being so coupled to said second potentiometer to reduce said difierence to a low value, whereby the voltage across said second potentiometer provides an electrical voltage representing the desired quotient.

7. A device for dividing two continuously variable quantities, including in combination:

a potentiometer having a resistance winding with one end connected to a reference point;

an arm of said potentiometer Whose position With respect to said reference point represents the divisor;

a voltage comparison means having first and second inputs for application of two voltages, said voltage comparison means comprising a pair of diodesconnected in series in the same polarity between said first and second inputs, said voltage comparison means providing at the junction of said diodes an output proportional to the difference between said two voltages;

an electrical connection connecting the arm of said potentiometer to said first input of said voltage comparison means;

a source of voltage representing the dividend, said source connected to said second input of said voltage 10 comparison means;

an amplifier;

an input circuit to said amplifier;

a source of alternating voltage applied to said amplifier input circuit;

means for coupling said comparison means output to said amplifier input circuit to control the amount of alternating voltage applied to said amplifier; and

means for rectifying the output of said amplifier and 8 for applying the rectified output to the remaining side of said potentiometer so that the voltage between said remaining side of said potentiometer and said reference point represents the quotient.

References Cited UNITED STATES PATENTS 6/1956 Langworthy 235-195 2,919,067 12/1959 Boyd 235196 OTHER REFERENCES Korn and Korn: Electronic Analog Computers, Mc-

Graw Hill, 1952 (QA, 76.4,K6), pp. 201, 231, and 232.

Assistant Examiners. 

1. A DEVICE FOR DIVIDING TWO VARIABLE QUANTITIES INCLUDING IN COMBINATION: A FIRST INPUT MEANS FOR CONNECTION OF A FIRST ELECTRICAL INPUT REPRESENTING THE FIRST OF SAID QUANTITIES AS A DIVIDEND, A SECOND INPUT MEANS FOR CONNECTION OF A SECOND ELECTRICAL INPUT REPRESENTING THE SECOND OF SAID QUANTITIES AS A DIVISOR, A POTENTIOMETER HAVING A RESISTANCE WINDING WITH ONE SIDE CONNECTED TO A REFERENCE POINT, AND HAVING A POTENTIOMETER ARM, A VOLTAGE COMPARISON MEANS HAVING FIRST AND SECOND INPUTS FOR CONNECTTION OF TWO INPUT VOLTAGE TO PROVIDE AN OUTPUT PROPORTIONAL TO THE DIFFERENCE BETWEEN SAID TWO VOLTAGES, MEANS COUPLED BETWEEN SAID SECOND INPUT MEANS AND SAID POTENTIOMETER ARM TO POSITION SAID ARM ALONG SAID RESISTANCE WINDING RELATIVE TO SAID REFERENCE POINT IN PROPORTION TO SAID SECOND ELECTRICAL INPUT, AN ELECTRICAL CONNECTION COUPLING SAID ARM OF SAID POTENTIOMETER TO THE FIRST INPUT OF SAID VOLTAGE COMPARISON MEANS, A SECOND ELECTRICAL CONNECTION COUPLING SAID FIRST INPUT MEANS TO THE SECOND INPUT OF SAID VOLTAGE COMPARISON MEANS, A HIGH GAIN AMPLIFIER HAVING AN INPUT COUPLED TO SAID VOLTAGE COMPARISON MEANS OUTPUT, SAID AMPLIFIER PROVIDING AN OUTPUT PROPORTIONAL TO SAID DIFFERENCE SIGNAL, AND MEANS INCLUDING A RECTIFIER FOR COUPLING THE OUTPUT OF SAID AMPLIFIER TO THE OTHER SIDE OF SAID RESISTANCE WINDING OF SAID POTENTIOMETER TO PROVIDE A VOLTAGE ON SAID ARM PROPORTIONAL TO THE PRODUCT OF SAID AMPLIFIER OUTPUT VOLTAGE AND SAID SECOND ELECTRICAL INPUT AS REPRESENTED BY THE POSITION OF SAID ARM OF SAID POTENTIOMETER TO REDUCE THE DIFFERENCE BETWEEN SAID VOLTAGE ON SAID ARM AND SAID FIRST ELECTRICAL INPUT TO A LOW VALUE, WHEREBY THE VOLTAGE ACROSS SAID POTENTIOMETER PROVIDES AN ELECTRICAL OUTPUT PROPORTIONAL TO A QUOTIENT. 